A population of rabbits oscillates 31 above and below averag

A population of rabbits oscillates 31 above and below average during the year, hitting the lowest value in January (t = 0). The average population starts at 600 rabbits and increases by 150 each year. Find an equation for the population, P, in terms of the months since January, t. P(t) =

Solution

P(t) = f(t) + g(t)

f(t) = cosine oscillation

period = 12 ;b = 2pi/12 = pi/6

f(t) = -31cos(pi*t/6)

g(t) = exponential function

% increase = 150/600 = 1/4 = 0.25

g(t) = 600(1+ .25)^t

P(t) = -31cos(pi*t/6) + 600(1.25)^t